88 research outputs found
Detecting Possible Manipulators in Elections
Manipulation is a problem of fundamental importance in the context of voting
in which the voters exercise their votes strategically instead of voting
honestly to prevent selection of an alternative that is less preferred. The
Gibbard-Satterthwaite theorem shows that there is no strategy-proof voting rule
that simultaneously satisfies certain combinations of desirable properties.
Researchers have attempted to get around the impossibility results in several
ways such as domain restriction and computational hardness of manipulation.
However these approaches have been shown to have limitations. Since prevention
of manipulation seems to be elusive, an interesting research direction
therefore is detection of manipulation. Motivated by this, we initiate the
study of detection of possible manipulators in an election.
We formulate two pertinent computational problems - Coalitional Possible
Manipulators (CPM) and Coalitional Possible Manipulators given Winner (CPMW),
where a suspect group of voters is provided as input to compute whether they
can be a potential coalition of possible manipulators. In the absence of any
suspect group, we formulate two more computational problems namely Coalitional
Possible Manipulators Search (CPMS), and Coalitional Possible Manipulators
Search given Winner (CPMSW). We provide polynomial time algorithms for these
problems, for several popular voting rules. For a few other voting rules, we
show that these problems are in NP-complete. We observe that detecting
manipulation maybe easy even when manipulation is hard, as seen for example, in
the case of the Borda voting rule.Comment: Accepted in AAMAS 201
Complexity of and Algorithms for Borda Manipulation
We prove that it is NP-hard for a coalition of two manipulators to compute
how to manipulate the Borda voting rule. This resolves one of the last open
problems in the computational complexity of manipulating common voting rules.
Because of this NP-hardness, we treat computing a manipulation as an
approximation problem where we try to minimize the number of manipulators.
Based on ideas from bin packing and multiprocessor scheduling, we propose two
new approximation methods to compute manipulations of the Borda rule.
Experiments show that these methods significantly outperform the previous best
known %existing approximation method. We are able to find optimal manipulations
in almost all the randomly generated elections tested. Our results suggest
that, whilst computing a manipulation of the Borda rule by a coalition is
NP-hard, computational complexity may provide only a weak barrier against
manipulation in practice
The Complexity of Manipulating -Approval Elections
An important problem in computational social choice theory is the complexity
of undesirable behavior among agents, such as control, manipulation, and
bribery in election systems. These kinds of voting strategies are often
tempting at the individual level but disastrous for the agents as a whole.
Creating election systems where the determination of such strategies is
difficult is thus an important goal.
An interesting set of elections is that of scoring protocols. Previous work
in this area has demonstrated the complexity of misuse in cases involving a
fixed number of candidates, and of specific election systems on unbounded
number of candidates such as Borda. In contrast, we take the first step in
generalizing the results of computational complexity of election misuse to
cases of infinitely many scoring protocols on an unbounded number of
candidates. Interesting families of systems include -approval and -veto
elections, in which voters distinguish candidates from the candidate set.
Our main result is to partition the problems of these families based on their
complexity. We do so by showing they are polynomial-time computable, NP-hard,
or polynomial-time equivalent to another problem of interest. We also
demonstrate a surprising connection between manipulation in election systems
and some graph theory problems
A Smooth Transition from Powerlessness to Absolute Power
We study the phase transition of the coalitional manipulation problem for
generalized scoring rules. Previously it has been shown that, under some
conditions on the distribution of votes, if the number of manipulators is
, where is the number of voters, then the probability that a
random profile is manipulable by the coalition goes to zero as the number of
voters goes to infinity, whereas if the number of manipulators is
, then the probability that a random profile is manipulable
goes to one. Here we consider the critical window, where a coalition has size
, and we show that as goes from zero to infinity, the limiting
probability that a random profile is manipulable goes from zero to one in a
smooth fashion, i.e., there is a smooth phase transition between the two
regimes. This result analytically validates recent empirical results, and
suggests that deciding the coalitional manipulation problem may be of limited
computational hardness in practice.Comment: 22 pages; v2 contains minor changes and corrections; v3 contains
minor changes after comments of reviewer
The Complexity of Online Manipulation of Sequential Elections
Most work on manipulation assumes that all preferences are known to the
manipulators. However, in many settings elections are open and sequential, and
manipulators may know the already cast votes but may not know the future votes.
We introduce a framework, in which manipulators can see the past votes but not
the future ones, to model online coalitional manipulation of sequential
elections, and we show that in this setting manipulation can be extremely
complex even for election systems with simple winner problems. Yet we also show
that for some of the most important election systems such manipulation is
simple in certain settings. This suggests that when using sequential voting,
one should pay great attention to the details of the setting in choosing one's
voting rule. Among the highlights of our classifications are: We show that,
depending on the size of the manipulative coalition, the online manipulation
problem can be complete for each level of the polynomial hierarchy or even for
PSPACE. We obtain the most dramatic contrast to date between the
nonunique-winner and unique-winner models: Online weighted manipulation for
plurality is in P in the nonunique-winner model, yet is coNP-hard (constructive
case) and NP-hard (destructive case) in the unique-winner model. And we obtain
what to the best of our knowledge are the first P^NP[1]-completeness and
P^NP-completeness results in the field of computational social choice, in
particular proving such completeness for, respectively, the complexity of
3-candidate and 4-candidate (and unlimited-candidate) online weighted coalition
manipulation of veto elections.Comment: 24 page
Complexity of Manipulation, Bribery, and Campaign Management in Bucklin and Fallback Voting
A central theme in computational social choice is to study the extent to
which voting systems computationally resist manipulative attacks seeking to
influence the outcome of elections, such as manipulation (i.e., strategic
voting), control, and bribery. Bucklin and fallback voting are among the voting
systems with the broadest resistance (i.e., NP-hardness) to control attacks.
However, only little is known about their behavior regarding manipulation and
bribery attacks. We comprehensively investigate the computational resistance of
Bucklin and fallback voting for many of the common manipulation and bribery
scenarios; we also complement our discussion by considering several campaign
management problems for Bucklin and fallback.Comment: 28 page
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